William is 3 times as old as Vanessa and is also 20 years older than Vanessa. How old is Vanessa?
Answer: We can use the given information to write down two equations that describe the ages of William and Vanessa. Let William's current age be $w$ and Vanessa's current age be $v$ $w = 3v$ $w = v + 20$ Now we have two independent equations, and we can solve for our two unknowns. Since we are looking for $v$ , and both of our equations have $w$ alone on one side, this is a convenient time to use elimination. Subtracting the second equation from the first equation, we get: $0 =$ $3v$ $-$ $ (v + 20)$ which combines the information about $v$ from both of our original equations. Solving for $v$ , we get: $2 v = 20$ $v = 10$.